Question

suppose a student wishes to minimize the objective function on a closed interval, but finds that it has only a single local maximum. where should the student look for the solution to the problem?

Answer 1

If there is only a single local maximum and the objective function needs to be minimized on a closed interval, the solution can be found at the boundaries of the interval.

Step-by-step explanation:

If a student wishes to minimize the objective function on a closed interval but finds that it has only a single local maximum, they should look for the solution at the boundaries of the closed interval. Since a local maximum is a point where the function reaches its highest value within a certain range, the boundaries are the only places where the global minimum can occur. By evaluating the function at the endpoints of the closed interval, the student can determine if one of them corresponds to the minimum value.

For example, if the closed interval is [0, 10] and the function has a single local maximum at x = 5, the student should check the values of the function at x = 0 and x = 10 to see if one of them is lower than the local maximum.

This approach is based on the fact that a local maximum may occur anywhere within the closed interval, but the global minimum can only occur at the boundaries.